Water at `20^(@)` is flowing in a pipe of radius `20.0 cm` . The viscosity of water at `20^(@)C` is `1.005` centipise. If the water's speed in the centre of the pipe is `3.00m//s`, what is water's speed:
(a) `10.0cm` from the centre of the pipe(half way between the centre and the walls)
(b) at the wall of the pipe?

Answer

A, B

Explanation

`v=(p_(1)-p_(2))/(4etaL) (R^(2)-r^(2))`
or, `v prop R^(2)-r^(2)`
(a) `(v_1)/(v_2)=(R^(2)-r_(1)^(2))/(R^(2)-r_(2)^(2))`
or, `(3)/(v_2)=(400-0)/(400-100)`
`:. v_(2)=2.25 m//s`
(b)`v_(2)=((R^(2)-r_(1)^(2))/(R^(2)-r_(1)^(2)))v_(1)`
`v_(2)=0 `at `r_(2)=R`.